limit as x approaches 0 of (sqrt(2(x+h(x)))-sqrt(2x))/(h(x))

解

x \to 0 lim (\frac{2 ( x + h ( x ) ) - 2 x}{h ( x )})

\frac{2}{h ( 0 )}

解答ステップ

x \to 0 lim (\frac{2 ( x + h ( x ) ) - 2 x}{h ( x )})

Plug in the value

x = 0

, assuming the function is continuous at this point

= \frac{2 ( 0 + h ( 0 ) ) - 2 \cdot 0}{h ( 0 )}

簡素化

\frac{2 ( 0 + h ( 0 ) ) - 2 \cdot 0}{h ( 0 )} : \frac{2}{h ( 0 )}

= \frac{2}{h ( 0 )}